Hi Samrat! Welcome to the site. As it stands I'm not sure how we can objectively give you a right or wrong answer. Can you help us out and tell us some more? Do you want to know how to make your Assasin do more damage? If you're stuck on how to ask a good question, check out the faq! :D
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PureferretJan 22 '12 at 16:09

2

It might also be helpful to give some details of the build you've chosen, including feats, powers etc.
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PhilJan 22 '12 at 16:31

3 Answers
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I don't think that the class is outright broken (as in "unplayable") but rather is seriously lacking feat/item support and requires a much higher level of expertise to properly build and play than other strikes (especially the ranger, where spamming Twin Strike is almost always the perfect answer to any problem -_-').

Anyway, there are some ways to increase the damage output of an assassin. The primary thing to remember, however, is that you will primarily deal large spikes of damage and not a high baseline damage every round (like e.g. a rogue).

Also note that an assassin can basically use the same tricks as other characters as well to pile up damage (using BFG-style weapons like the executioner's axe or the fullblade, knocking prone for Headsman's Chop[DDI], using a Frost Weapon[DDI] for frost cheese, using items like Gauntlets of Blood[DDI] for more damage against bloodied targets, and so on and so forth).

Feats

Cruel Shroud[DDI]: gain CA against targets under your shroud; works well in combination with Power Attack[DDI] and two-handed weapons to effectively gain a substantial free damage boost

Killer's Insight[DDI]: once per encounter add 2 shrouds with single use of the Assassin's Shroud power

Powers

Shadow Storm[DDI]: level 1 at-will; attack deals 1 (2 at epic tier) additional damage for each creature adjacent to the target (this does include the assassin himself!); depending on your party composition this can produce a good damage bonus

Targeted for Death[DDI]: level 1 daily; as an effect until the end of the encounter you add 2 shrouds when you use the Assassin's Shroud power against the target

Twilight Assassin[DDI]: level 5 daily; conjure shadow assassin that can make minor action implement melee attacks (Dex vs Ref, 3 damage or 6 damage if target has shroud on it); useful for crit-fishing since you can make 3 attacks per round now (standard + 2x minor)

Guild of Shadows[DDI]: level 19 daily; basically the same as with Twilight Assassin but this is the multi-target version; you summon 3 shadow assassins that make an implement melee attack against one adjacent enemy (Dex vs Ref, 5+Dex mod damage) when you sustain the power as a minor action - the only drawback is that your duplicates cannot attack the same target

Soul of Death[DDI]: level 22 daily utility; regain hit points as if you had spent a surge and additionally use Assassin's Shroud up to 4 times against a visible enemy; drawback: it's an interrupt that triggers when you drop to 0

Doom Foretold[DDI]: level 29 daily; not only the probably biggest gun in the assassin's arsenal at 7[W] but also let's you use Assassin's Shroud up to 4 times against the target after the attack; useful for building chains: add 4 shrouds in any way > attack with this power > immediately have 4 shrouds again > spend action point and attack with other daily/encounter

Items

Death Shroud Ki Focus[DDI]: level 4+; encounter free-action power that lets you use Assassin's Shroud on the hit target and doesn't count against the 1/round limitation; also deals additional critical damage for each shroud on the target (invoked or not)

Bracers of Assassination[DDI]: level 16+; score critical hits on 19-20 when using an assassin/assassin paragon path attack power against targets with 3+ shrouds; the level 26 version increases the range to 18-20

I've had no problems producing Striker Damage with my original assassin.

As a Drow you should comfortably have 18 Dex 18 Cha.

The 3 feats I think are most important to my character's success are; Sneak of Shadows (you can reliably get CA as an Assassin giving you a 1/Enc +2d6), Killer Instinct (gets that 2nd Shroud down round 1), and Light Blade Expertise (again easy to get CA).

With Shadow Storm you should be getting 1d8+4+4+1 every round as a base, get a flank with a buddy and you have 1d8+4+4+2+1. Never build more than 2 Shrouds except if you used Killer Instinct.

For Theme the Unseelie Agent is an excellent choice for Assassins; it gives you a summonable +1 weapon at level 1. (OK its great for everyone but the whole "I'm unarmed but can summon a weapon when I want it" thing thematically fits the Assassin.) This will propel you to 1d8+4+4+1+1 as a base damage.

Finally the Death Shroud Ki Focus is the "go to" Ki Focus for the the Assassin. It lets you put an extra shroud on a creature after you have hit it - with your Shrouds already declared as being used.

This build lets you do a turn 1 spike damage (if you can get CA) of 2[w]+4+4+1+1+2d6+3d6. That's pretty safe striker damage. Sure you drop down to 1[w]+10 as your base after that but you should be able to routinely get an extra 2d6+1 damage on that.

If you take Two_weapon fighting (and get a Rhythm Blade for your off-hand) you get another +1 damage.

You can also access Nimble Blade for an extra +1 to hit making it more likely you will add your Shrouds more likely to be triggered.

To raise an exception to your wording, the assassin is not "broken" in the normal sense of the word (game-breakingly over-powered) but is broken in the "lying on pieces on the floor" sense. It does not compete in damage, though its mobility options are exceptional. It is, however, worth noting that a strong stealth empahsis on your party can make assassins quite effective. Unfortunately, in typical tactics an Assassin doing its thing is the equivalent of a hacker in SR3 shadowrun: while they do their thing, the rest of the group goes and gets pizza.

My recommendation is to call a different class an assassin. A shade (race) or rogue cunning stalker will give necessary "assassiny" stealth while allowing non-zero damage. An essentials drow thief can be quite exceptional in combat, considering the damage output of drow feats on crossbows. If you provide your build, I will attempt to recreate its playstyle in a class that doesn't suck. (In fact, I've already statted a base drow "assassin" here)

The executioner assasin from Heroes of Shadow is more competitive in terms of contributing in combat, I believe. Well, compared to the original assasin, not the thief, which is exceptional.
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adamjfordJan 22 '12 at 20:29

The executioner assassin is merely sub-par from the perspective of DPR. However, I would happily play one in a group not particularly worried about damage as I love the flavour (especially of the ninja).
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Brian Ballsun-Stanton♦Jan 22 '12 at 21:46

It has low DPR too? Lame. Agreed about happily playing one anyway, though.
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adamjfordJan 23 '12 at 15:36

@adamjford it requires significant optimization to bring its DPR to "okay" standpoints when compared to the other strikers. Low, is as ever, a function of the specific game.
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Brian Ballsun-Stanton♦Jan 23 '12 at 17:40